Progress in Mathematics

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

Authors: BARTOCCI, CLAUDIO, Bruzzo, Ugo, Hernández Ruipérez, Daniel

  • Provides an expository account of Fourier–Mukai and Nahm Transforms
  • Includes recent developments for which no thorough account exists
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About this book

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character.

Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph.

Key features:

* Basic constructions and definitions are presented in preliminary background chapters

* Presentation explores applications and suggests several open questions

* Extensive bibliography and index

This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.

Reviews

From the reviews:

“The main aim of the book under review is to study a class of functors between derived categories of coherent sheaves of smooth varieties, known as integral (or, in some cases, Fourier-Mukai) functors. Recently, this subject is rapidly developing and the book under review contains a valuable survey of the known results. … the book is very well written and it will certainly be very useful to researchers in algebraic geometry and mathematical physics.” (Adrian Langer, Zentralblatt MATH, Vol. 1186, 2010)

“The monograph under review surveys the developments in the subject since Mukai’s original discovery, mainly concentrating on geometric aspects. … the authors do a good job of being precise while at the same time remaining readable. … there are appendices on background material, including triangulated categories, as well as a final outlook section on stability conditions, making the presentation self-contained and also largely complete in terms of recent developments. … more accessible to graduate students and working mathematicians … .”­­­ (Balázs Szendrői, Mathematical Reviews, Issue 2010 k)


Table of contents (11 chapters)

  • Integral functors

    Bartocci, Claudio (et al.)

    Pages 1-30

  • Fourier-Mukai functors

    Bartocci, Claudio (et al.)

    Pages 31-79

  • Fourier-Mukai on Abelian varieties

    Bartocci, Claudio (et al.)

    Pages 81-109

  • Fourier-Mukai on K3 surfaces

    Bartocci, Claudio (et al.)

    Pages 111-146

  • Nahm transforms

    Bartocci, Claudio (et al.)

    Pages 147-182

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-0-8176-4663-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-0-8176-3246-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics
Authors
Series Title
Progress in Mathematics
Series Volume
276
Copyright
2009
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4663-9
DOI
10.1007/b11801
Hardcover ISBN
978-0-8176-3246-5
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XVI, 418
Number of Illustrations and Tables
83 b/w illustrations
Topics